### Abstract

Contests in nature are frequently won by the animal with the higher resource holding potential (RHP), consistent with animals assessing opponents' RHP accurately. Nevertheless, RHP asymmetry can determine a contest without any assessment of opponents' RHP. To establish this result, we develop an analytical model of the war of attrition for an arbitrary distribution of initial RHP. If its coefficient of variation, κ, is sufficiently high or if cost of persistence per unit time is sufficiently small compared with the rate at which a victor can translate its remaining reserves into fitness, then there is a unique evolutionarily stable strategy (ESS) at which - despite no assessment - the victor is always the animal with higher RHP. Thus victory by the contestant with higher RHP does not by itself imply that an animal assesses its opponent's RHP accurately. Data from a damselfly, Calopteryx maculata, suggest that re is large enough for the ESS to exist when RHP is determined by energy reserves. We identify characteristics of the ESS that may help to clarify whether animals 'observe' (via any sensory modality) a difference in physical magnitudes by comparing separate perceptions of each magnitude (Hypothesis A) or by perceiving the difference itself(Hypothesis B). First, a critical value of κ, above which the ESS invariably exists, exceeds a half under Hypothesis A but is less than a third under Hypothesis B; its precise value depends weakly on the initial RHP distribution. Second, the ESS distributions of final RHP among winners and losers both have a lower mean and higher variance under Hypothesis A than under Hypothesis B. Third, the ESS distribution of contest duration times has a lower mean and higher variance under Hypothesis B than under Hypothesis A. All derived distributions are determined analytically for arbitrary initial RHP.

Original language | English (US) |
---|---|

Pages (from-to) | 65-83 |

Number of pages | 19 |

Journal | Journal of Theoretical Biology |

Volume | 181 |

Issue number | 1 |

DOIs | |

State | Published - Jul 7 1996 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Journal of Theoretical Biology*,

*181*(1), 65-83. https://doi.org/10.1006/jtbi.1996.0115

}

*Journal of Theoretical Biology*, vol. 181, no. 1, pp. 65-83. https://doi.org/10.1006/jtbi.1996.0115

**On wars of attrition without assessment.** / Mesterton-Gibbons, Michael; Marden, James Harold; Dugatkin, Lee Alan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On wars of attrition without assessment

AU - Mesterton-Gibbons, Michael

AU - Marden, James Harold

AU - Dugatkin, Lee Alan

PY - 1996/7/7

Y1 - 1996/7/7

N2 - Contests in nature are frequently won by the animal with the higher resource holding potential (RHP), consistent with animals assessing opponents' RHP accurately. Nevertheless, RHP asymmetry can determine a contest without any assessment of opponents' RHP. To establish this result, we develop an analytical model of the war of attrition for an arbitrary distribution of initial RHP. If its coefficient of variation, κ, is sufficiently high or if cost of persistence per unit time is sufficiently small compared with the rate at which a victor can translate its remaining reserves into fitness, then there is a unique evolutionarily stable strategy (ESS) at which - despite no assessment - the victor is always the animal with higher RHP. Thus victory by the contestant with higher RHP does not by itself imply that an animal assesses its opponent's RHP accurately. Data from a damselfly, Calopteryx maculata, suggest that re is large enough for the ESS to exist when RHP is determined by energy reserves. We identify characteristics of the ESS that may help to clarify whether animals 'observe' (via any sensory modality) a difference in physical magnitudes by comparing separate perceptions of each magnitude (Hypothesis A) or by perceiving the difference itself(Hypothesis B). First, a critical value of κ, above which the ESS invariably exists, exceeds a half under Hypothesis A but is less than a third under Hypothesis B; its precise value depends weakly on the initial RHP distribution. Second, the ESS distributions of final RHP among winners and losers both have a lower mean and higher variance under Hypothesis A than under Hypothesis B. Third, the ESS distribution of contest duration times has a lower mean and higher variance under Hypothesis B than under Hypothesis A. All derived distributions are determined analytically for arbitrary initial RHP.

AB - Contests in nature are frequently won by the animal with the higher resource holding potential (RHP), consistent with animals assessing opponents' RHP accurately. Nevertheless, RHP asymmetry can determine a contest without any assessment of opponents' RHP. To establish this result, we develop an analytical model of the war of attrition for an arbitrary distribution of initial RHP. If its coefficient of variation, κ, is sufficiently high or if cost of persistence per unit time is sufficiently small compared with the rate at which a victor can translate its remaining reserves into fitness, then there is a unique evolutionarily stable strategy (ESS) at which - despite no assessment - the victor is always the animal with higher RHP. Thus victory by the contestant with higher RHP does not by itself imply that an animal assesses its opponent's RHP accurately. Data from a damselfly, Calopteryx maculata, suggest that re is large enough for the ESS to exist when RHP is determined by energy reserves. We identify characteristics of the ESS that may help to clarify whether animals 'observe' (via any sensory modality) a difference in physical magnitudes by comparing separate perceptions of each magnitude (Hypothesis A) or by perceiving the difference itself(Hypothesis B). First, a critical value of κ, above which the ESS invariably exists, exceeds a half under Hypothesis A but is less than a third under Hypothesis B; its precise value depends weakly on the initial RHP distribution. Second, the ESS distributions of final RHP among winners and losers both have a lower mean and higher variance under Hypothesis A than under Hypothesis B. Third, the ESS distribution of contest duration times has a lower mean and higher variance under Hypothesis B than under Hypothesis A. All derived distributions are determined analytically for arbitrary initial RHP.

UR - http://www.scopus.com/inward/record.url?scp=0030573540&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030573540&partnerID=8YFLogxK

U2 - 10.1006/jtbi.1996.0115

DO - 10.1006/jtbi.1996.0115

M3 - Article

AN - SCOPUS:0030573540

VL - 181

SP - 65

EP - 83

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 1

ER -